The Dunedin City Council has called the damage "selfish" and says it is now too late to resow the grass until later in the year.
Photos and a video of the go-kart driving around Chingford Park were posted on social media at the weekend with the caption "literally tearing it up in a go-kart at Chingford Park".
It has since been removed.
Sam Caldwell, who made the post, said the caption was "a little bit tongue-in-cheek".
"It seemed like an unusual occurrence, to witness something like that happening in Chingford Park, which is usually a pretty peaceful, quiet park.
"They were also doing quite a bit of damage to the ground there, tearing around and muddying up the grass, making it potentially a little bit difficult to walk through certain areas."
The go-kart flung up dirt and grass as it accelerated and spun around corners, and he believed there were more appropriate places to use it.
A man claiming to be the driver’s father later privately messaged Mr Caldwell, demanding the post be removed.
The man said he would be "seeing u round mate [oncoming fist emoji]" and called Mr Caldwell a "b...." and a "nark".
Mr Caldwell said he felt "quite taken aback" being threatened with physical violence by a stranger, and had since filed a police report.
The response seemed accusatory and "a bit over the top".
"Perhaps my tone or the reason why I posted it was misconstrued, thinking that I was pointing blame or anything like that.
"It was just an interesting thing to witness on my little evening stroll."
He did not believe anybody could be identified from the video.
Chingford Park was a public space and a go-kart being driven around was "an activity that’s not the norm for that space".
"So it’s to be expected that people may film or take photos of those sorts of activities."
A council spokesman confirmed there was surface damage to the ground at Chingford Park, and that go-karts were not permitted on the grass under the Reserves and Beaches Bylaw 2017.
The ruts would need to be levelled out and the grass resown, but it was too late in the season to resow the grass now and so it would need to happen later in the year.
"It’s really disappointing to see this sort of selfish behaviour, which impacts on everyone’s enjoyment of our reserves.
"As well as being a popular sports and recreational facility, Chingford Park is often booked for weddings and other significant events precisely because of its beautiful, natural surroundings.
"Anything that disrupts that is a blow for the people who treasure the area, and all ratepayers are left to cover the cost."
Senior Sergeant Anthony Bond, of Dunedin, said police were called to Chingford Park about 5.30pm on Sunday.
It was reported a 15-year-old boy was driving around the area "ripping up the grass".
Officers spoke to the teen and his father and advised the pair to be mindful of driving at the park as it could cause damage, Snr Sgt Bond said.
